Asymptotic stabilization of planar unstable linear systems by a finite number of saturating actuators

This work is devoted to stabilization of unstable continuous-time linear systems in the presence of saturating actuators. We show that, if the state matrix has real eigenvalues, it is possible to construct a linear feedback such that the set of values satysfying the saturation constraint is an invariant set for the closed-loop system. Moreover, once the initial datum is arbitrarily fixed, we can ensure asymptotic stabilization of the system splitting the control variable in a predefined number of saturating components. A design technique for a controller having such invariance property is also given for discrete linear systems.